Why is the quran as well as some hadiths considered perfectly preserved while other hadiths are not?

Salam everyone. I read a question about a proof of the authenticity of the quran : https://islam.stackexchange.com/questions/36210/prove-it-to-me-that-the-quran-is-perfectly-preserved . In short, the answers and comments globally say it cannot be proven. If that is so, then why are some hadiths and the quran usually considered perfectly preserved ? I know the quran itself says it is. But the fact that it is written in it doesn't prevent it from being modified, the part saying it is preserved being left untouched. I also think it could explain a lot. I see lots of efforts done to change its translation/interpretation in order to make it more compliant to either science or humanist morals. Common aspects in this case are the creation myth, aicha's age when she married the prophet (pbuh), the treatment of apostates/slaves/non muslims, the status of women, ... It seems to me it would make more sense to say that the people of that time modified god's message to fit their own earthly purposes. Why is this option never considered publicly (I heard it from a friend in private) ?